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XL Y III. Note on the Action of Coupled Circuits and 

 Mechanical Analogies. By H. C. Plummer *. 



1. ri^HE paper by Prof. Barton and Miss Browning 

 JL (p. 246) suggests a doubt whether a simple elec- 

 trical problem really is made easier for the average student 

 by a complicated mechanical analogy. It seems as if the 

 avowed purpose is to remedy the difficulty o£ one problem 

 not only by setting another but by requiring the relation 

 between the two to be understood. Yet surely the real 

 difficulty begins, and almost ends, in the electrical problem, 

 in establishing the fundamental equations. The mechanical 

 analogy does not assist in this but only in the subsequent 

 interpretation. 



Curiously enough, the authors do not seem to have pre- 

 sented their analogies in the clearest light. Thus, for 

 example, their equations (27) and (28) may be re-written in 

 the form 



The analogy is now exact, and requires 



tp- z P + Q + /3P *tq_* P + Q+ffQ 

 u *-g' P + Q ' g' P + Q ' 



-MR= Z .A, -MS= Z ^ P 



P + Q' — </'P + Q' 



which give for the coupling 



/3 2 PQ 



7 = 



(P + Q+0P)(P + Q+£Q)' 



more distinctly than the authors seem to have shown. At 

 the same time LR — NS = M(R — S), a limitation of the con- 

 ditions apparently overlooked. The second analogy does 

 not suffer from the same defect, but in general terms is even 

 more complicated. The coupling may be made positive by 

 reversing the sign of y or z. 



* Communicated by the Author. 



